pow_zero

Exact expanded PA statement

forall a e n. e = 0 -> (exists ff_b_z ff_c_z. ((forall ff_i_z_repeat. (exists ff_lt_z_repeat_bound. ff_lt_z_repeat_bound + S ff_i_z_repeat = e) -> (((exists ff_h_z_repeat_decoded. ff_h_z_repeat_decoded + S (a) = S ((S (ff_i_z_repeat)) * ff_c_z)) /\ exists ff_q_z_repeat_decoded. ff_b_z = ff_q_z_repeat_decoded * S ((S (ff_i_z_repeat)) * ff_c_z) + (a)))) /\ (exists ff_u_z_product ff_v_z_product. ((((exists ff_h_z_product_start. ff_h_z_product_start + S (1) = S ((S (0)) * ff_v_z_product)) /\ exists ff_q_z_product_start. ff_u_z_product = ff_q_z_product_start * S ((S (0)) * ff_v_z_product) + (1))) /\ ((((exists ff_h_z_product_terminal. ff_h_z_product_terminal + S (n) = S ((S (e)) * ff_v_z_product)) /\ exists ff_q_z_product_terminal. ff_u_z_product = ff_q_z_product_terminal * S ((S (e)) * ff_v_z_product) + (n))) /\ forall ff_i_z_product. (exists ff_lt_z_product_bound. ff_lt_z_product_bound + S ff_i_z_product = e) -> exists ff_p_z_product ff_r_z_product ff_s_z_product. ((((exists ff_h_z_product_factor. ff_h_z_product_factor + S (ff_p_z_product) = S ((S (ff_i_z_product)) * ff_c_z)) /\ exists ff_q_z_product_factor. ff_b_z = ff_q_z_product_factor * S ((S (ff_i_z_product)) * ff_c_z) + (ff_p_z_product))) /\ ((((exists ff_h_z_product_partial. ff_h_z_product_partial + S (ff_r_z_product) = S ((S (ff_i_z_product)) * ff_v_z_product)) /\ exists ff_q_z_product_partial. ff_u_z_product = ff_q_z_product_partial * S ((S (ff_i_z_product)) * ff_v_z_product) + (ff_r_z_product))) /\ ((((exists ff_h_z_product_successor. ff_h_z_product_successor + S (ff_s_z_product) = S ((S (S ff_i_z_product)) * ff_v_z_product)) /\ exists ff_q_z_product_successor. ff_u_z_product = ff_q_z_product_successor * S ((S (S ff_i_z_product)) * ff_v_z_product) + (ff_s_z_product))) /\ ff_s_z_product = ff_r_z_product * ff_p_z_product)))))))) -> n = 1